The Kondo effect is a cornerstone in the study of strongly correlated fermions. The coherent exchange coupling of conduction electrons to local magnetic moments gives rise to a Kondo cloud that screens the impurity spin. Here we report on the interplay between spin–orbit interaction and the Kondo effect, that can lead to a underscreened Kondo effects in quantum dots in bilayer graphene. More generally, we introduce a different experimental platform for studying Kondo physics. In contrast to carbon nanotubes, where nanotube chirality determines spin–orbit coupling breaking the SU(4) symmetry of the electronic states relevant for the Kondo effect, we study a planar carbon material where a small spin–orbit coupling of nominally flat graphene is enhanced by zero-point out-of-plane phonons. The resulting two-electron triplet ground state in bilayer graphene dots provides a route to exploring the Kondo effect with a small spin–orbit interaction.

We investigate low-temperature transport through single InAs quantum wells and broken-gap InAs/GaSb double quantum wells. Non-local measurements in the regime beyond bulk pinch-off confirm the presence of edge conduction in InAs quantum wells. The edge resistivity of 1-2 kΩ/µm is of the same order of magnitude as edge resistivities measured in the InAs/GaSb double quantum well system. Measurements in tilted magnetic field suggests an anisotropy of the conducting regions at the edges with a larger extent in the plane of the sample than normal to it. Finger gate samples on both material systems shine light on the length dependence of the edge resistance with the intent to unravel the nature of edge conduction in InAs/GaSb coupled quantum wells.

Transport measurements are performed on InAs/GaSb double quantum wells at zero and finite magnetic fields applied parallel and perpendicular to the quantum wells. We investigate a sample in the inverted regime where electrons and holes coexist, and compare it with another sample in the non-inverted semiconducting regime. Activated behavior in conjunction with a strong suppression of the resistance peak at the charge neutrality point in a parallel magnetic field attest to the topological hybridization gap between electron and hole bands in the inverted sample. We observe an unconventional Landau level spectrum with energy gaps modulated by the magnetic field applied perpendicular to the quantum wells. This is caused by strong spin-orbit interaction provided jointly by the InAs and the GaSb quantum wells.

Pauli blockade mechanisms-whereby carrier transport through quantum dots (QD) is blocked due to selection rules even when energetically allowed-are a direct manifestation of the Pauli exclusion principle, as well as a key mechanism for manipulating and reading out spin qubits. The Pauli spin blockade is well established for systems such as GaAs QDs, but is to be further explored for systems with additional degrees of freedom, such as the valley quantum numbers in carbon-based materials or silicon. Here we report experiments on coupled bilayer graphene double quantum dots, in which the spin and valley states are precisely controlled, enabling the observation of the two-electron combined blockade physics. We demonstrate that the doubly occupied single dot switches between two different ground states with gate and magnetic-field tuning, allowing for the switching of selection rules: with a spin-triplet-valley-singlet ground state, valley blockade is observed; and with the spin-singlet-valley-triplet ground state, robust spin blockade is shown.

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